Atnaujinkite slapukų nuostatas

El. knyga: Discrete Systems with Memory [World Scientific e-book]

(Etsi Agronomos, Spain)
Kitos knygos pagal šią temą:
  • World Scientific e-book
  • Kaina: 184,80 €*
  • * this price gives unlimited concurrent access for unlimited time
Discrete Systems with MemoryDidesnis paveikslėlis
Kitos knygos pagal šią temą:
World Scientific e-booksMore info about World Scientific e-books
Partnerių interneto svetainė: http://www.worldscientific.com/worldscibooks/10.1142/8119#t=toc
Memory is a universal function of organized matter. What is the mathematics of memory? How does memory affect the space-time behaviour of spatially extended systems? Does memory increase complexity? This book provides answers to these questions.It focuses on the study of spatially extended systems, i.e., cellular automata and other related discrete complex systems. Thus, arrays of locally connected finite state machines, or cells, update their states simultaneously, in discrete time, by the same transition rule. The classical dynamics in these systems is Markovian: only the actual configuration is taken into account to generate the next one.Generalizing the conventional view on spatially extended discrete dynamical systems evolution by allowing cells (or nodes) to be featured by some trait state computed as a function of its own previous state-values, the transition maps of the classical systems are kept unaltered, so that the effect of memory can be easily traced.The book demonstrates that discrete dynamical systems with memory are not only priceless tools for modeling natural phenomena but unique mathematical and aesthetic objects.
Preface vii
1 Cellular Automata and memory
1(6)
1.1 Cellular Automata
1(3)
1.2 Memory
4(3)
Disclaimer
5(2)
2 Average type memory
7(32)
2.1 Average memory
7(2)
2.2 Two-dimensional lattices
9(8)
2.2.1 Totalistic rules
9(4)
2.2.2 LIFE
13(4)
2.3 One-dimensional layers
17(22)
2.3.1 Elementary rules
17(16)
2.3.2 Nearest and next-nearest neighbors
33(6)
3 Other memories
39(42)
3.1 Average-like memory
39(6)
3.2 Limited trailing memory
45(2)
3.3 Majority of the last three state memory
47(14)
3.4 Elementary rules as memory
61(12)
3.5 Minimal memory
73(8)
4 Asynchrony and probabilistic rules
81(14)
4.1 Asynchrony
81(3)
4.2 Probabilistic rules
84(11)
5 Cycles and random sequences
95(10)
5.1 Cycles
95(3)
5.2 Random number generation by CA
98(7)
6 Three state automata
105(16)
6.1 Totalistic rules
105(8)
6.2 Excitable systems
113(8)
7 Reversible dynamics
121(22)
7.1 Characterization
121(2)
7.2 Reversible rules with memory
123(20)
8 Block cellular automata
143(16)
8.1 Characterization
143(2)
8.2 Density classification task
145(14)
9 Structurally dynamic systems
159(16)
9.1 Introduction
159(4)
9.1.1 Reversible SDCA
161(2)
9.2 SDCA with memory
163(12)
9.2.1 Two state SDCA with memory
163(4)
9.2.2 Three state SDCA
167(8)
10 Boolean networks
175(28)
10.1 Automata on networks
175(8)
10.2 Boolean networks
183(7)
10.3 Automata on proximity graphs
190(13)
11 Coupled layers
203(28)
11.1 Coupled cellular automata
203(17)
11.2 Coupled Boolean networks
220(11)
12 Continuous state variable
231(40)
12.1 Continuous-valued automata
231(3)
12.2 Finite difference equations
234(16)
12.2.1 One-dimensional maps
234(12)
12.2.2 Two-dimensional maps
246(4)
12.3 Plane curves
250(18)
12.4 Stochastic processes
268(3)
13 Spatial games
271(72)
13.1 The prisoner's dilemma
271(15)
13.2 Degrees of cooperation and strategies
286(9)
13.3 The structurally dynamic PD (SDPD)
295(23)
13.4 Pavlov versus anti-Pavlov (PAP) in the PD
318(7)
13.5 Other spatial games
325(18)
Appendices
Appendix A Average memory starting at random
343(8)
Appendix B Dynamic with short-term memory
351(20)
Appendix C Heterogeneous and coupled networks
371(18)
Appendix D Continuous state variable
389(14)
Appendix E Spatial games
403(26)
Bibliography 429(22)
List of Figures 451(10)
List of Tables 461(2)
Index 463
Pastovi nuoroda: https://www.kriso.lt/db/9789814343640_pe.html